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It's almost impossible to put a figure on it in computer memory terms. In a linear (conventional) computer, each byte can hold only 1 of 2 values (0 or 1) & each byte is discrete insofar as its content and action is not dependent on the value of any other byte. Memory in the brain doesn't work like that.There are approximately 100 billion neurons (brain cells) in the adult human brain and they are intricately linked. Some are associated with memory, others with autonomic functions such as breathing, yet others serve different purposes again. Those that are associated with memory are intricately linked to many others (up to 10,000) and each 1 can participate in many memories.Even if as few as 1% of neurons are associated with memory, that means an effective 1 billion x 10,000 connections (10,000,000,000,000). If each connection of each neuron = 1 part of a memory, that equates to 10 thousand terabytes. However, it's not quite as simple as that.It is thought that neurons can participate in different memories as a result of the levels of neurotransmitters they produce at any given time. So, not only can each neuron connect to 10,000 others, but they can affect those others differently depending on the level of neurotransmitter they produce. It is almost beyond imagination how complicated such a network is, and how many possible memories it could store.I'm not a neuroscientist, so I have given a very simplistic explanation which others here may take exception to. However, I think it gives a rough idea of the difficulty of answering your question.
There are sciences that doesn't require too much insight into physical matter but is...well, admit it, bordering on non-being a science (like history).